AdrianP: The justification for the 16. d5! pawn sac doesn't become apparent until 20. d7!! sacs a piece out of the blue. Kaspy must have calculated to the end from move 16. d5! Who else would have seen such an attack from such a comparatively innocuous position...

acirce: Some comments from John Watson’s “Chess Strategy in Action”, the section “The Positional Pawn Sacrifice”:

16.d5! <Giving up a pawn for the sake of a single soon-to-be-isolated passed pawn. Kasparov remarks that pawn sacrifices of this type are frequently seen in GM games today as opposed to traditional chess and even in contrast to the partially Karpov-influenced style of the 1980s. In his words, “the new generation says that initiative can be worth material and that this is more appreciated than before.” He claims that he himself “contributed to the changing philosophy.” Indeed, I remember being surprised time and again by Kasparov’s early pawn sacrifices, which were quite unlike ones that I was used to. But these are fast-moving times, and today such a sacrifice looks almost routine and is often passed over without even an ‘!’, so deeply have such ideas penetrated our thinking.>

20.d7!! <This piece sacrifice is the real justification for 16.d5!, a fact that emphasizes the need for calculation. It ‘cuts the board in two’, a favourite Kasparov theme.>

22.Nxg5 <Interestingly, the same fellow making this sacrifice argues that most of Tal’s combinations would be refuted today by top grandmasters “because the defensive technique is on an absolutely different level”. Although some grandmasters of the time doubted its soundness, Kasparov’s sacrifice was later shown to be airtight. That has proven true of most of his gifts throughout the years.>

26.d8=Q!! <Giving up the pride of White’s position, but for concrete attacking purposes, in spite of the reduced material.>

Etc – Watson gives some alternative ways for Black to lose but there has to be much more exhaustive analysis somewhere else. Stohl's book? Plus I wanted to focus on the verbal commentary here, telling us something about both Kasparov (to think that he was only 16 years old here!) and chess development in general.

20 d7! After the solid 20 Bf4 White has a promising position, but still nothing decisive after 20 ...Nb8!? (20 ... Rad8 21 Re1! is worse for Black) Kasparov increases the tension with a further sacrifice and afterwords he freely admits he was led more by intuition than pure calculation. Analysis proves him right - although Black could have played better at more than one point, the sacrifice is correct.

20 ... fxg5? This is consistent but very greedy [Stohl gives 20. ...Kh8; 20. ...Rad8 and 20. ...Nb4!? as alternatives]

"Bronstein recalls that later many of the tournament participants spent a long time trying to demonstrate that the bishop sacrifice was incorrect; Geller was especially agitated, being convinced that any attack should be properly prepared. The situation is familiar to me: when i won an attractive game against Pribyl with a piece sacrifice [Skara 1980], my older colleagues observing the game- Karpov, Vaganian and others- also spent a long time seeking a refutation, some 'hole'. It is evident that brilliance by others provokes a certain inner dissatisfaction: why can't I do that?"
[OMGP vol. 2 game no. 58]

Looking at this game i don't see anything wrong with Kasparov's illustrious older colleagues. After the bishop sac, the position indeed makes for a fascinating case study. I don't think Karpov was trying to refute it just because he was jealous. He was probably trying to uphold his chess principles by refuting a premature sacrifice by his classical, positional standards. That the sacrifice is alright shows that Kasparov's handling of the attack was by no means premature or anti-positional. He simply thought in a different, more dynamic [and also more brilliant] category that was ahead of his time!

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